EBS customers should ensure that they are running JRE 7u10, at minimum, on Windows desktop clients.

Of
the compatibility issues identified with JRE 7, the most
critical is an issue that prevents E-Business Suite Forms-based products
from launching on Windows desktops that are running JRE 7.

Customers can prevent this issue -- and all other JRE 7 compatibility issues -- by ensuring
that they have applied the latest certified patches documented for JRE 7
configurations to their EBS application tier servers. These are summarized here for convenience. If the requirements change over time, please check the Notes for the authoritative list of patches:

These patches are compatible with JRE 6 and 7, production ready,
and fully-tested with the E-Business Suite. These patches may be
applied immediately to all E-Business Suite environments. All other
Forms prerequisites documented in the Notes above should also be applied.

Where are the official patch requirements documented?

All
patches required for ensuring full compatibility of the E-Business
Suite with JRE 7 are documented in these Notes:

No need to worry -- it's fixed. To recap: JRE releases 1.6.0_18
through 1.6.0_22 had issues with mismanaging session cookies that affected some users in some circumstances.

The fix for those issues was first included in JRE 1.6.0_23. These
fixes will carry forward and continue to be fixed in all future JRE
releases on the JRE 6 and 7 codelines. In other words, if you wish to avoid the mismanaged session
cookie issue, you should apply any release after JRE 1.6.0_22 on the JRE 6 codeline, and JRE 7u10 and later JRE 7 codeline updates.

All JRE 6 and 7 releases are certified with EBS upon release

Our standard policy is that all E-Business Suite customers can apply all
JRE updates to end-user desktops from JRE 1.6.0_03 and later updates on the 1.6 codeline, and from JRE 7u10 and later updates on the JRE 7 codeline. We test
all new JRE 1.6 and JRE 7 releases in parallel with the JRE development process, so
all new JRE 1.6 and 7 releases are considered certified with the E-Business Suite on
the same day that they're released by our Java team.

You do not need to wait for a certification announcement before
applying new JRE 1.6 or JRE 7 releases to your EBS users' desktops.

The latest updates to that page (as of Sept. 19, 2012) state (emphasis added):

Java SE 6 End of Public Updates Notice

After February 2013, Oracle will no longer post updates of Java SE 6 to
its public download sites. Existing Java SE 6 downloads already posted
as of February 2013 will remain accessible in the Java Archive
on Oracle Technology Network. Developers and end-users are encouraged
to update to more recent Java SE versions that remain available for
public download. For enterprise customers, who need continued access to
critical bug fixes and security fixes as well as general maintenance for
Java SE 6 or older versions, long term support is available through Oracle Java SE Support .

What does this mean for Oracle E-Business Suite users?

EBS users fall under the category of "enterprise users" above.
Java is an integral part of the Oracle E-Business Suite technology
stack, so EBS users will continue to receive Java SE 6 updates after
February 2013.

In other words, nothing will change for EBS users after February 2013.

EBS users will continue to receive critical bug fixes and security
fixes as well as general maintenance for Java SE 6. These Java SE 6
updates will be made available to EBS users for the Extended Support
periods documented in the Oracle Lifetime Support policy document for Oracle Applications (PDF):

EBS 11i Extended Support ends November 2013

EBS 12.0 Extended Support ends January 2015

EBS 12.1 Extended Support ends December 2018

How can EBS customers obtain Java 6 updates after the public end-of-life?

Will EBS users be forced to upgrade to JRE 7 for Windows desktop clients?

No. This upgrade is highly recommended but currently remains
optional. JRE 6 will be available to Windows users to run with EBS for
the duration of your respective EBS Extended Support period. Updates
will be delivered via My Oracle Support, where you can continue to
receive critical bug fixes and security fixes as well as general
maintenance for JRE 6 desktop clients.

Coexistence of JRE 6 and JRE 7 on Windows desktops

The upgrade to JRE 7 is highly recommended for EBS users, but
some users may need to run both JRE 6 and 7 on their Windows desktops
for reasons unrelated to the E-Business Suite.

Most EBS configurations
with IE and Firefox use non-static versioning by default. JRE 7 will
be invoked instead of JRE 6 if both are installed on a Windows desktop.
For more details, see "Appendix B: Static vs. Non-static Versioning and
Set Up Options" in Notes 290807.1 and 393931.1.

Auto-update will only keep JRE 7 up-to-date for Windows users with both JRE 6 and 7 installed.

JRE 6 users are strongly encouraged to apply the latest Critical
Patch Updates as soon as possible after each release. The Jave SE CPUs
will be available via My Oracle Support. EBS users can find more
information about JRE 6 and 7 updates here:

Will EBS users be forced to upgrade to JDK 7 for EBS application tier servers?

No. This upgrade will be highly recommended but will be optional
for EBS application tier servers running on Windows, Linux, and
Solaris. You can
choose to remain on JDK 6 for
the duration of your respective EBS Extended Support period. If you
remain on JDK 6, you will continue to receive critical bug fixes and
security fixes as well as general maintenance for JDK 6.

The certification of Oracle E-Business Suite with JDK 7 for EBS
application tier servers on Windows, Linux, and Solaris as well as other
platforms such as IBM AIX and HP-UX is planned. Customers running
platforms other than Windows, Linux, and Solaris should refer to their
Java vendors's sites for more information about their support policies.